Bae's bullet-riddled body was found on Wednesday, the day South Korean media said he would have turned 42.
The Taliban said the South Korean government had not been acting in good faith and threatened to kill more of the Korean hostages if its demands were not met.
Bae, a married man with a nine-year-old daughter, was from a devout Christian family from the island province of Jeju. He went to theology school and became a pastor about six years ago.
Bae, whose father is a church elder in Jeju, was a founding member of the Saemmul Church south of Seoul, which sent the volunteers to Afghanistan. He led services for younger members of its congregation, reports quoted people who knew him as saying.
"He was close to many members of the church, because he was always generous enough to help with the prayers of each of the 300 members of the youth division," Yonhap news quoted an acquaintance as saying.
He is believed to have suffered from a respiratory ailment but he was well enough to lead the group abroad, a Saemmul church official said.
Bae was travelling on a bus with 22 other Koreans -- 18 of whom are women -- when Taliban insurgents took the group hostage on Friday on the main road south from Kabul.
Bae was the oldest member of the group that went despite warnings from Seoul not to go due to security concerns.
A Taliban spokesman said Bae had been killed in a desert area in the Qarabagh district of Ghazni close to where the group had been abducted.
